
We note that FNO actually starkly resembles a two-layer CNN, where the first layer consists of a convolutional layer with full circulant padding and a global convolutional kernel. Unlike a typical CNN, in which the kernel size is usually small and the convolution is local, the convolution here is much larger, which means there are many more parameters than a typical CNN. Similar CNN architectures have previously been analyzed via convex duality [1]}, [2]}. Accordingly, for both linear and ReLU activation, (REF ) is equivalent to a convex optimization problem.
